Question

determine whether the function is even, odd or neither

Answer 1

\[f(x) = x (\sin ^{3}x)\]

Answer 2

start by finding f(-x)
if u get f(-x) = f(x) then the function is even
if u get f(-x) = -f(x) then the function is odd
if dont get any of above, then its neither

Answer 3

\(f(x) = x (\sin ^{3}x)\)

\(f(-x) = (-x) (\sin ^{3}(-x))\)

simplify

Answer 4

use this : \(\sin(-x) = -\sin(x)\)

Answer 5

so its odd?

Answer 6

\(f(x) = x (\sin ^{3}x)\)

\(f(-x) = (-x) (\sin ^{3}(-x))\)

\(f(-x) = (-x) (\sin (-x))^3\)

\(f(-x) = (-x) (-\sin (x))^3\)

\(f(-x) = (-x) (-1)^3 (\sin^3 (x))\)

\(f(-x) = (-x) (-1) (\sin^3 (x))\)

\(f(-x) = x (\sin^3 (x))\)

\(f(-x) = f(x) \)

Answer 7

EVEN !

Answer 8

wow i got confused there but with each step it makes more sense...thank you!

Answer 9

good :)